diff --git a/lib/transfer.c b/lib/transfer.c
index 8b28b1e629..fcc4006af3 100644
--- a/lib/transfer.c
+++ b/lib/transfer.c
@@ -1637,7 +1637,7 @@ CURLcode Curl_follow(struct Curl_easy *data,
 
   if((type != FOLLOW_RETRY) &&
      (data->req.httpcode != 401) && (data->req.httpcode != 407) &&
-     Curl_is_absolute_url(newurl, NULL, 0))
+     Curl_is_absolute_url(newurl, NULL, 0, FALSE))
     /* If this is not redirect due to a 401 or 407 response and an absolute
        URL: don't allow a custom port number */
     disallowport = TRUE;
@@ -1649,8 +1649,11 @@ CURLcode Curl_follow(struct Curl_easy *data,
                     CURLU_ALLOW_SPACE |
                     (data->set.path_as_is ? CURLU_PATH_AS_IS : 0));
   if(uc) {
-    if(type != FOLLOW_FAKE)
+    if(type != FOLLOW_FAKE) {
+      failf(data, "The redirect target URL could not be parsed: %s",
+            curl_url_strerror(uc));
       return Curl_uc_to_curlcode(uc);
+    }
 
     /* the URL could not be parsed for some reason, but since this is FAKE
        mode, just duplicate the field as-is */
diff --git a/lib/url.c b/lib/url.c
index 3d65925236..4a3a0e50c8 100644
--- a/lib/url.c
+++ b/lib/url.c
@@ -1995,7 +1995,7 @@ static CURLcode parseurlandfillconn(struct Curl_easy *data,
     return CURLE_OUT_OF_MEMORY;
 
   if(data->set.str[STRING_DEFAULT_PROTOCOL] &&
-     !Curl_is_absolute_url(data->state.url, NULL, 0)) {
+     !Curl_is_absolute_url(data->state.url, NULL, 0, TRUE)) {
     char *url = aprintf("%s://%s", data->set.str[STRING_DEFAULT_PROTOCOL],
                         data->state.url);
     if(!url)
diff --git a/lib/urlapi-int.h b/lib/urlapi-int.h
index 5d9db8ccc7..43a83ef6e4 100644
--- a/lib/urlapi-int.h
+++ b/lib/urlapi-int.h
@@ -25,7 +25,8 @@
  ***************************************************************************/
 #include "curl_setup.h"
 
-size_t Curl_is_absolute_url(const char *url, char *buf, size_t buflen);
+size_t Curl_is_absolute_url(const char *url, char *buf, size_t buflen,
+                            bool guess_scheme);
 
 #ifdef DEBUGBUILD
 CURLUcode Curl_parse_port(struct Curl_URL *u, struct dynbuf *host,
diff --git a/lib/urlapi.c b/lib/urlapi.c
index baecb84b92..2276b93dd4 100644
--- a/lib/urlapi.c
+++ b/lib/urlapi.c
@@ -184,8 +184,12 @@ static CURLUcode strcpy_url(struct dynbuf *o, const char *url, bool relative)
  * Returns the length of the scheme if the given URL is absolute (as opposed
  * to relative). Stores the scheme in the buffer if TRUE and 'buf' is
  * non-NULL. The buflen must be larger than MAX_SCHEME_LEN if buf is set.
+ *
+ * If 'guess_scheme' is TRUE, it means the URL might be provided without
+ * scheme.
  */
-size_t Curl_is_absolute_url(const char *url, char *buf, size_t buflen)
+size_t Curl_is_absolute_url(const char *url, char *buf, size_t buflen,
+                            bool guess_scheme)
 {
   int i;
   DEBUGASSERT(!buf || (buflen > MAX_SCHEME_LEN));
@@ -193,7 +197,7 @@ size_t Curl_is_absolute_url(const char *url, char *buf, size_t buflen)
   if(buf)
     buf[0] = 0; /* always leave a defined value in buf */
 #ifdef WIN32
-  if(STARTS_WITH_DRIVE_PREFIX(url))
+  if(guess_scheme && STARTS_WITH_DRIVE_PREFIX(url))
     return 0;
 #endif
   for(i = 0; i < MAX_SCHEME_LEN; ++i) {
@@ -207,7 +211,11 @@ size_t Curl_is_absolute_url(const char *url, char *buf, size_t buflen)
       break;
     }
   }
-  if(i && (url[i] == ':') && (url[i + 1] == '/')) {
+  if(i && (url[i] == ':') && ((url[i + 1] == '/') || !guess_scheme)) {
+    /* If this does not guess scheme, the scheme always ends with the colon so
+       that this also detects data: URLs etc. In guessing mode, data: could
+       be the host name "data" with a specified port number. */
+
     /* the length of the scheme is the name part only */
     size_t len = i;
     if(buf) {
@@ -934,7 +942,9 @@ static CURLUcode parseurl(const char *url, CURLU *u, unsigned int flags)
     goto fail;
   }
 
-  schemelen = Curl_is_absolute_url(url, schemebuf, sizeof(schemebuf));
+  schemelen = Curl_is_absolute_url(url, schemebuf, sizeof(schemebuf),
+                                   flags & (CURLU_GUESS_SCHEME|
+                                            CURLU_DEFAULT_SCHEME));
 
   /* handle the file: scheme */
   if(schemelen && !strcmp(schemebuf, "file")) {
@@ -1059,11 +1069,6 @@ static CURLUcode parseurl(const char *url, CURLU *u, unsigned int flags)
         p++;
         i++;
       }
-      if((i < 1) || (i>3)) {
-        /* less than one or more than three slashes */
-        result = CURLUE_BAD_SLASHES;
-        goto fail;
-      }
 
       schemep = schemebuf;
       if(!Curl_builtin_scheme(schemep) &&
@@ -1072,6 +1077,11 @@ static CURLUcode parseurl(const char *url, CURLU *u, unsigned int flags)
         goto fail;
       }
 
+      if((i < 1) || (i>3)) {
+        /* less than one or more than three slashes */
+        result = CURLUE_BAD_SLASHES;
+        goto fail;
+      }
       if(junkscan(schemep, flags)) {
         result = CURLUE_BAD_SCHEME;
         goto fail;
@@ -1730,7 +1740,9 @@ CURLUcode curl_url_set(CURLU *u, CURLUPart what,
     /* if the new thing is absolute or the old one is not
      * (we could not get an absolute url in 'oldurl'),
      * then replace the existing with the new. */
-    if(Curl_is_absolute_url(part, NULL, 0)
+    if(Curl_is_absolute_url(part, NULL, 0,
+                            flags & (CURLU_GUESS_SCHEME|
+                                     CURLU_DEFAULT_SCHEME))
        || curl_url_get(u, CURLUPART_URL, &oldurl, flags)) {
       return parseurl_and_replace(part, u, flags);
     }